An elementary proof of the following theorem is given:
THEOREM. Let M be a compact connected surface without boundary. Consider a C∞ action of Rn on M. Then, if the Euler-Poincaré characteristic of M is non zero there exists a fixed point.
@article{urn:eudml:doc:41091, title = {An elementary proof of a Lima's theorem for surfaces.}, journal = {Publicacions Matem\`atiques}, volume = {33}, year = {1989}, pages = {555-557}, zbl = {0698.57011}, mrnumber = {MR1038490}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41091} }
Turiel Sandín, Francisco Javier. An elementary proof of a Lima's theorem for surfaces.. Publicacions Matemàtiques, Tome 33 (1989) pp. 555-557. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41091/